Defense lawyers said the far-right militia had assembled ahead of the Jan. 6 attack on the Capitol to await what they hoped would be a decision by Donald Trump to invoke the Insurrection Act.
The perception that lawmakers are cashing in on their offices has fueled cynicism among voters. Some politicians want to take the current limits further.
The archives said in a letter to the House Oversight Committee that it was seeking electronic messages from unnamed White House officials sent through personal accounts.
The measure passed on an overwhelming bipartisan vote, the last action in the House before lawmakers departed to campaign ahead of the November midterm elections.